Apps which I've found useful whilst in Japan are "imi wa?", a popular Japanese-English dictionary, "Google Maps" for getting around those narrows streets, and "Hyperdia" for train times all over Japan (it seems there is a 30 day limit on it though, fine for vacations, although the website doesn't have a time usage limit - I mostly use that).
Google Translate has been my best friend, especially since it was just updated with the Camera input. On most occasions, I can get menus translated from Japanese --> English by simply taking a photo. The app will scan and then highlight words to translate, or you can highlight by swiping the screen with your finger. Voice input or Handwriting input works great too!
100% agree that the Hyperdia app is great for trains. You just have to know exact train station names for input, so be sure to determine points A to B, ensure correct spelling, and include hyphens.
Not too sure aobut communication...but Hyperdia is probably one of the most useful ones out there. Especially if you're a tourist - you can include the option for 'JR pass' on that, and it helps you calculate the cheapest/fastest route and stuff. Check it out!
Here in Kyushu, I've been starting to track the apps put out by the surrounding prefectures. Saga Prefecture has an EXCELLENT app (Dogan Shitato) where you can even ring someone on the spot to help with translation assistance. The Kagoshima Travel Guide app is also pretty useful. Neither is good if you're just sticking to the "Golden Route" of Japan, but if you're Kyushu bound, I say they're more than worth checking out. And they're free.
I recommend MyMizu app, Japan's first water refill app showing nearby water fountains, environment-friendly shops, and other places to fill your bottle with drinkable water for free, reducing your expenses and your consumption of plastic bottles.